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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
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package org.bouncycastle.crypto.engines;

import java.math.BigInteger;
import java.security.SecureRandom;

import org.bouncycastle.crypto.AsymmetricBlockCipher;
import org.bouncycastle.crypto.CipherParameters;
import org.bouncycastle.crypto.CryptoServicesRegistrar;
import org.bouncycastle.crypto.DataLengthException;
import org.bouncycastle.crypto.params.ParametersWithRandom;
import org.bouncycastle.crypto.params.RSAKeyParameters;
import org.bouncycastle.crypto.params.RSAPrivateCrtKeyParameters;
import org.bouncycastle.util.BigIntegers;

/**
 * this does your basic RSA algorithm with blinding
 */
public class RSABlindedEngine
    implements AsymmetricBlockCipher
{
    private static final BigInteger ONE = BigInteger.valueOf(1);

    private RSACoreEngine    core = new RSACoreEngine();
    private RSAKeyParameters key;
    private SecureRandom     random;

    /**
     * initialise the RSA engine.
     *
     * @param forEncryption true if we are encrypting, false otherwise.
     * @param param the necessary RSA key parameters.
     */
    public void init(boolean forEncryption, CipherParameters parameters)
    {
        SecureRandom providedRandom = null;
        if (parameters instanceof ParametersWithRandom)
        {
            ParametersWithRandom withRandom = (ParametersWithRandom)parameters;
            providedRandom = withRandom.getRandom();
            parameters = withRandom.getParameters();
        }

        core.init(forEncryption, parameters);

        this.key = (RSAKeyParameters)parameters;
        this.random = initSecureRandom(key instanceof RSAPrivateCrtKeyParameters, providedRandom);
    }

    /**
     * Return the maximum size for an input block to this engine.
     * For RSA this is always one byte less than the key size on
     * encryption, and the same length as the key size on decryption.
     *
     * @return maximum size for an input block.
     */
    public int getInputBlockSize()
    {
        return core.getInputBlockSize();
    }

    /**
     * Return the maximum size for an output block to this engine.
     * For RSA this is always one byte less than the key size on
     * decryption, and the same length as the key size on encryption.
     *
     * @return maximum size for an output block.
     */
    public int getOutputBlockSize()
    {
        return core.getOutputBlockSize();
    }

    /**
     * Process a single block using the basic RSA algorithm.
     *
     * @param in the input array.
     * @param inOff the offset into the input buffer where the data starts.
     * @param inLen the length of the data to be processed.
     * @return the result of the RSA process.
     * @exception DataLengthException the input block is too large.
     */
    public byte[] processBlock(byte[] in, int inOff, int inLen)
    {
        if (key == null)
        {
            throw new IllegalStateException("RSA engine not initialised");
        }

        BigInteger input = core.convertInput(in, inOff, inLen);
        BigInteger result = processInput(input);
        return core.convertOutput(result);
    }

    protected SecureRandom initSecureRandom(boolean needed, SecureRandom provided)
    {
        return needed ? CryptoServicesRegistrar.getSecureRandom(provided) : null;
    }

    private BigInteger processInput(BigInteger input)
    {
        if (key instanceof RSAPrivateCrtKeyParameters)
        {
            RSAPrivateCrtKeyParameters crtKey = (RSAPrivateCrtKeyParameters)key;

            BigInteger e = crtKey.getPublicExponent();
            if (e != null)   // can't do blinding without a public exponent
            {
                BigInteger m = crtKey.getModulus();

                BigInteger r = BigIntegers.createRandomInRange(ONE, m.subtract(ONE), random);
                BigInteger blind = r.modPow(e, m);
                BigInteger unblind = BigIntegers.modOddInverse(m, r);

                BigInteger blindedInput = blind.multiply(input).mod(m);
                BigInteger blindedResult = core.processBlock(blindedInput);
                return unblind.multiply(blindedResult).mod(m);
            }
        }

        return core.processBlock(input);
    }
}